The moment maps in diffeology
April 21, 2007, update May 3, 2008
In this memoir, I give a generalization of the moment maps for the category {Diffeology}. This construction applies to every smooth action of a diffeological group  G on a diffeological space X, equipped with a closed 2-form ω. I exhibit a universal construction for the whole group of automorphisms Diff(X,ω) associated to every  pair (X,ω). The key fact of this construction is that it avoids any reference to Lie algebra or to any notion of vector fields. It introduces and uses only the space of momenta of a diffeological
group, that is the space of its left-invariant 1-forms. These constructions are illustrated by some examples, some suggested by the mathematical literature.

Published as a Memoir of the American Mathematical Society, vol. 207 (2010), no. 972. If you have some remark, send me a email...